WASHINGTON — After ruling against Texas officials in two recent cases involving the death penalty, the Supreme Court accepted a third case Monday from a Texas death row inmate.

The justices agreed to hear an appeal by Carlos Ayestas, a Honduran national who has been on Texas’ death row for 19 years.

They sent two additional cases involving Texas death row inmates back to lower courts for re-evaluation, in light of the court’s ruling last week that the state’s standards for evaluating intellectual disability are unconstitutional.

Ayestas was sentenced to death for his role in a 1995 home invasion in which he and two others bound Santiaga Paneque, a 67-year-old woman, with duct tape. Before leaving the house, the three men strangled Paneque to death.

Ayestas received the death penalty, but his new legal team says his original trial lawyer was ineffective. In a brief, his lawyers noted that he had a history of drug abuse and presented "red flags for mental health problems."

"Trial counsel failed to follow up on any of those leads," lawyer Lee Kovarsky wrote.

But lawyers for the state of Texas argue that Ayestas has been granted all the legal assistance to which he is constitutionally entitled. Further, they say, Ayestas has been examined by psychologists and dealt with a series of investigators.

The Supreme Court will determine if Ayestas should be given more resources to investigate whether his original lawyer ignored key aspects of his life that might have persuaded the jury to give him a life sentence instead of the death penalty.

“This case boils down to the right to effective assistance of counsel,” said Kate Black, a member of Ayestas’ legal team from the Texas Defender Service. “And when you don’t have that, getting the resources to be able to prove it.”

Attorney General Ken Paxton declined to comment on the Supreme Court’s decision to hear Ayestas’ appeal.

The justices' other recent rulings against Texas officials include one in February in favor of Duane Buck, a 53-year-old inmate who, like Ayestas, has been on death row for 19 years. At Buck’s original sentencing trial, a psychologist testified that he was at “increased risk for future dangerousness” specifically because he is black.

In a 6-2 ruling, the justices ruled that Buck should be allowed to continue his appeal. Chief Justice John Roberts wrote that it was clear the sentencing hearing involved racially biased testimony, which he called a “toxin.”

Last week, the justices also invalidated Texas’ method for evaluating intellectual disability in death row inmates. For 13 years, state courts have relied on a process that combined medical standards from 1992 with additional nonscientific factors to determine if inmates are intellectually fit for execution.

Lawyers for Bobby Moore, who has been on death row for more than 36 years, argued that Moore is intellectually disabled by modern medical standards. The Supreme Court ruled in his favor and sent his case back to lower courts for re-evaluation.

On Monday, the Supreme Court sent two additional Texas death row cases back to lower courts as a result of their decision in the Moore case. Death row inmates James Henderson and Raymond Martinez will have their cases re-evaluated.